Copyright | (c) Andrew Lelechenko 2014-2020 |
---|---|

License | GPL-3 |

Maintainer | andrew.lelechenko@gmail.com |

Safe Haskell | None |

Language | Haskell2010 |

Linear programming over exponent pairs

Package implements an algorithm to minimize the maximum of a list of rational objective functions over the set of exponent pairs. See full description in A. V. Lelechenko, Linear programming over exponent pairs. Acta Univ. Sapientiae, Inform. 5, No. 2, 271-287 (2013). http://www.acta.sapientia.ro/acta-info/C5-2/info52-7.pdf

A set of useful applications can be found in Math.ExpPairs.Ivic, Math.ExpPairs.Kratzel and Math.ExpPairs.MenzerNowak.

## Synopsis

- optimize :: [RationalForm Rational] -> [Constraint Rational] -> OptimizeResult
- data OptimizeResult
- optimalValue :: OptimizeResult -> RationalInf
- optimalPair :: OptimizeResult -> InitPair
- optimalPath :: OptimizeResult -> Path
- simulateOptimize :: Rational -> OptimizeResult
- simulateOptimize' :: RationalInf -> OptimizeResult
- data LinearForm t
- data RationalForm t = (LinearForm t) :/: (LinearForm t)
- data IneqType
- data Constraint t
- type InitPair = InitPair' Rational
- data Path
- data RatioInf t
- type RationalInf = RatioInf Integer
- pattern K :: (Eq a, Num a) => a -> LinearForm a
- pattern L :: (Eq a, Num a) => a -> LinearForm a
- pattern M :: (Eq a, Num a) => a -> LinearForm a
- (>.) :: Num t => LinearForm t -> LinearForm t -> Constraint t
- (>=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t
- (<.) :: Num t => LinearForm t -> LinearForm t -> Constraint t
- (<=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t
- scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t

# Documentation

optimize :: [RationalForm Rational] -> [Constraint Rational] -> OptimizeResult Source #

This function takes a list of rational forms and a list of constraints and returns an exponent pair, which satisfies all constraints and minimizes the maximum of all rational forms.

data OptimizeResult Source #

Container for the result of optimization.

## Instances

Eq OptimizeResult Source # | |

Defined in Math.ExpPairs (==) :: OptimizeResult -> OptimizeResult -> Bool # (/=) :: OptimizeResult -> OptimizeResult -> Bool # | |

Ord OptimizeResult Source # | |

Defined in Math.ExpPairs compare :: OptimizeResult -> OptimizeResult -> Ordering # (<) :: OptimizeResult -> OptimizeResult -> Bool # (<=) :: OptimizeResult -> OptimizeResult -> Bool # (>) :: OptimizeResult -> OptimizeResult -> Bool # (>=) :: OptimizeResult -> OptimizeResult -> Bool # max :: OptimizeResult -> OptimizeResult -> OptimizeResult # min :: OptimizeResult -> OptimizeResult -> OptimizeResult # | |

Show OptimizeResult Source # | |

Defined in Math.ExpPairs showsPrec :: Int -> OptimizeResult -> ShowS # show :: OptimizeResult -> String # showList :: [OptimizeResult] -> ShowS # | |

Pretty OptimizeResult Source # | |

Defined in Math.ExpPairs pretty :: OptimizeResult -> Doc ann # prettyList :: [OptimizeResult] -> Doc ann # |

optimalValue :: OptimizeResult -> RationalInf Source #

The minimal value of objective function.

optimalPair :: OptimizeResult -> InitPair Source #

The initial exponent pair, on which minimal value was achieved.

optimalPath :: OptimizeResult -> Path Source #

The sequence of processes, after which minimal value was achieved.

simulateOptimize :: Rational -> OptimizeResult Source #

Wrap `Rational`

into `OptimizeResult`

.

simulateOptimize' :: RationalInf -> OptimizeResult Source #

Wrap `RationalInf`

into `OptimizeResult`

.

data LinearForm t Source #

Define an affine linear form of three variables: a*k + b*l + c*m.
First argument of `LinearForm`

stands for a, second for b
and third for c. Linear forms form a monoid by addition.

## Instances

data RationalForm t Source #

Define a rational form of two variables, equal to the ratio of two `LinearForm`

.

(LinearForm t) :/: (LinearForm t) infix 5 |

## Instances

Constants to specify the strictness of `Constraint`

.

## Instances

Bounded IneqType Source # | |

Enum IneqType Source # | |

Defined in Math.ExpPairs.LinearForm | |

Eq IneqType Source # | |

Ord IneqType Source # | |

Defined in Math.ExpPairs.LinearForm | |

Show IneqType Source # | |

Generic IneqType Source # | |

Pretty IneqType Source # | |

Defined in Math.ExpPairs.LinearForm | |

type Rep IneqType Source # | |

data Constraint t Source #

A linear constraint of two variables.

## Instances

Holds a list of `Process`

and a matrix of projective
transformation, which they define.

## Instances

Eq Path Source # | |

Ord Path Source # | |

Read Path Source # | |

Show Path Source # | |

Generic Path Source # | |

Semigroup Path Source # | |

Monoid Path Source # | |

Pretty Path Source # | |

Defined in Math.ExpPairs.Process | |

type Rep Path Source # | |

Defined in Math.ExpPairs.Process type Rep Path = D1 (MetaData "Path" "Math.ExpPairs.Process" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" False) (C1 (MetaCons "Path" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 ProcessMatrix) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 [Process]))) |

Extend `Ratio`

`t`

with \( \pm \infty \) positive and negative
infinities.

## Instances

Eq t => Eq (RatioInf t) Source # | |

Integral t => Fractional (RatioInf t) Source # | |

Integral t => Num (RatioInf t) Source # | |

Defined in Math.ExpPairs.RatioInf | |

Integral t => Ord (RatioInf t) Source # | |

Integral t => Real (RatioInf t) Source # | |

Defined in Math.ExpPairs.RatioInf toRational :: RatioInf t -> Rational # | |

Show t => Show (RatioInf t) Source # | |

(Integral t, Pretty t) => Pretty (RatioInf t) Source # | |

Defined in Math.ExpPairs.RatioInf |

type RationalInf = RatioInf Integer Source #

Arbitrary-precision rational numbers with positive and negative infinities.

(>.) :: Num t => LinearForm t -> LinearForm t -> Constraint t infix 5 Source #

Build a constraint, which states that the value of the first linear form is greater than the value of the second one.

(>=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t infix 5 Source #

Build a constraint, which states that the value of the first linear form is greater or equal to the value of the second one.

(<.) :: Num t => LinearForm t -> LinearForm t -> Constraint t infix 5 Source #

Build a constraint, which states that the value of the first linear form is less than the value of the second one.

(<=.) :: Num t => LinearForm t -> LinearForm t -> Constraint t infix 5 Source #

Build a constraint, which states that the value of the first linear form is less or equal to the value of the second one.

scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t Source #

Multiply a linear form by a given coefficient.